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# Simplifying (an equation with a fraction within a fraction)

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1. I find it difficult to simplify an equation which has a fraction within a fraction. For example, I do not understand how to simplify this:

Apparently, this can be rewritten as this:

But I do not understand the process used to achieve this. I would be grateful if someone could take me through the process of simplifying this equation and perhaps help me to understand a general method for simplifying equations involving a fraction within a fraction.
2. (Original post by Stikki)
I find it difficult to simplify an equation which has a fraction within a fraction. For example, I do not understand how to simplify this:

Apparently, this can be rewritten as this:

But I do not understand the process used to achieve this. I would be grateful if someone could take me through the process of simplifying this equation and perhaps help me to understand a general method for simplifying equations involving a fraction within a fraction.
If you multiply the entire fraction by (x+1)/(x+1) [which does not change the value since it is equal to 1] you find that the numerator becomes x+1 and the denominator becomes 1+x+1=x+2

Hence we can write it as
3. Another way is

Find a common denominator for the bottom

Simplify

Then just remembering division of fractions, 1 divided by a fraction is the same as 1 times the reciprocal.
4. take the denominator:

(1/(x+1)) + 1

you can multiply the 1 by (x+1)/(x+1) to make it:

(1/(x+1)) + (x+1)/(x+1)

now both fractions in the denominator have a common denominator of x+1, so turn it into one fraction:

(1/(x+1)) + (x+1)/(x+1) = (1+(x+1))/(x+1)

which simplifies to (x+2)/(x+1)

so the fraction is now 1/((x+2)/(x+1))

as i assume you know, you can take the denominator of the denominator and stick it on the numerator to turn this into:

(x+1)/(x+2)

voila
5. do the smallest one frst, if that makes sense:

6. I understand how it works now. Thank you everyone.
7. (Original post by Prokaryotic_crap)
do the smallest one frst, if that makes sense:

Wouldn't it be better to times through by x+1 to begin as it can get confusing with remembering which line is more prevalent?
8. (Original post by Stikki)

Hence,

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